Journal of Theoretical Probability

, Volume 29, Issue 1, pp 292–306 | Cite as

Strong Mixing and Operator-Selfdecomposability

  • Richard C. BradleyEmail author
  • Zbigniew J. Jurek


For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met (an “infinitesimality” assumption, and a restriction to “full” distributions), the possible limit distributions are precisely the operator-self-decomposable laws.


Strong mixing Operator self-decomposability Urbanik semigroup 

Mathematics Subject Classification

Primary 60B10 60E07 60F05 Secondary 15A16 20M20 



The authors thank the referee and the associate editor for their helpful comments, which improved the exposition.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Institute of MathematicsUniversity of WrocławWrocławPoland

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